Developing a scale to measure factors influencing skier’s self-perceived group dynamics (FISSGD)

Data Wrangling

For the interest of space, codes in this section will not be shown. Yet they are available in the .rmd file.

Read in the data

The data were collected across years 2022 (CARE panel, n=218) and 2023 (Students joining an avalanche course, n =59).

Combine 2022 and 2023 data

They were combined into one data set (n = 277). An index variable was generated as the unique identifier for each case.

Reomove cases

Remove careless responses (according to attention trap)

Q10_2 and Q10_5, as well as Q19_1 and Q19_4 were same questions with different wordings. If the responses had conflictory results between them, they would be regarded as careless responses and hence deleted (n = 24).

Remove cases who did not consent

Respondents who did not consent to participate were removed from the data (n = 4).

Remove cases with NA for if having a leader

Respondents who did not disclose if the ski group had a leader were removed from the data (n = 27).

Replace value of -99 with NA

-99 was used to label seen but unanswered questions. They were relabeled as NA.

Unify value labels

Values of some of the variables had been inconsistently labeled by Qualtrics. They were unified here.

Relabel variables

Properly label the variables so that the interpretation can be better managed. For the label, see Table 1.

Unify the direction of item wording

Four items of the SOCIAL were worded in negative direction (e.g. XXXX). Basic factor analysis attempts to identify latent variance through exploring the co-variance in measured variables. As such, the direction of the item wording (positive vs negative) does not influence the analysis. However, we still unify the results into same wording direction (positive) for the interest of easy interpretation.

Generate Norwegian variable labels

The survey was carried out in Norwegian and the initial language of text is Norwegian. Norwegian labels were created here.

Create data sets for analysis

Four data sets were created. They are a. 18 item with leader; b. 6 item with leader; c. 17 item without leader; d. 5 item without leader; 3. background. The case identifier is “index” variable across data sets.

Create with-leader and without-leader data-sets

Before generating 4 data sets, the data were first separated according to with (n = 104) or with-out leader (n = 118).

Remove cases with 50% NAs across major questions for each data sets

Within in each data set (with/without leader), cases with 50% NAs were removed from data. Three cases (#213,253,276) were removed from with-leader group; Four cases (#94, 252, 258, 275) were removed from without-leader group.

Create data set: 17 item without leader

Without-leader group respondents answered 22 out of 26 questions in the survey (the remaining 4 questions were about leader). Within the 22 questions, 17 were adapted from Zeiweiful’s long version, 5 were from short version. They were further split into two data sets. They were subsequently referred to as without-leader long and without-leader short, respectively. The sample size is 114. According the publications, the minimum sample size for an exploratory factor analysis should be 5 × (number of items). In our case, the without-leader group’s long version analysis involves 17 items, indicating at least 17×5=85 samples. Our sample size meets this requirement.

Create data set: 5 item without leader

According the publications, the minimum sample size for an exploratory factor analysis should be 5 × (number of items). In our case, the without-leader group’s long version analysis involves 5 items, indicating at least 5×5=25 samples. Our sample size meets this requirement.

Create data set: 20 item with leader

Without-leader group respondents answered all 26 questions in the survey. Among the questions, 20 were adapted from Zeiweiful’s long version, 6 were from short version. They were further split into two data sets. They were subsequently referred to as with-leader long and with-leader short, respectively. The sample size is 101. According the publications, the minimum sample size for an exploratory factor analysis should be 5 × (number of items). In our case, the without-leader group’s long version analysis involves 20 items, indicating at least 20×5=100 samples. Our sample size meets this requirement.

Create data set: 6 item with leader

According the publications, the minimum sample size for an exploratory factor analysis should be 5 × (number of items). In our case, the without-leader group’s long version analysis involves 5 items, indicating at least 6×5=30 samples. Our sample size meets this requirement.

Check and impute NAs and IDNs

Discritpive statistics with number of NAs and IDNs for each item

Descriptive statistics for with-leader group (long)

					Central tendency		Dispersion tendency
var	Question	n*	n of IDN†	n of NA	Mean	Median	SD	Q1~Q3
i_leader2	The leader (formal or informal) communicated openly and clearly	100	2	1	4.3	4.0	0.8	4.0 ~ 5.0
i_leader3	Everyone could voice their concerns to the leader (formal or informal)	100	3	1	4.6	5.0	0.7	4.0 ~ 5.0
i_skill1	The least knowledgeable group member could conduct satisfactory avalanche assessments for this trip	101	1	0	3.2	4.0	1.3	2.0 ~ 4.0
i_skill2	There was no large gap in avalanche assessment skills between the group members	101	2	0	2.5	2.0	1.3	1.0 ~ 4.0
i_skill3	There was no important difference in skiing skill level between group members, given the terrain	101	1	0	2.9	3.0	1.4	2.0 ~ 4.0
i_skill4	All group members were equipped with standard avalanche safety equipment (beacon, shovel, probe) and trained in the use of it	101	2	0	4.3	5.0	1.1	4.0 ~ 5.0
i_orga1	The group members knew each other well	101	0	0	3.8	4.0	1.2	3.0 ~ 5.0
i_orga2	The group size was appropriate for the trip (time, difficulty)	100	1	1	4.5	5.0	0.8	4.0 ~ 5.0
i_orga3	The roles of the group members were clearly defined	101	1	0	3.2	3.0	1.2	2.0 ~ 4.0
i_comm1	Decisions concerning avalanche hazard were well discussed in the group	101	1	0	4.1	4.0	0.9	4.0 ~ 5.0
i_comm2	Everyone in the group understood the decisions that were made	101	4	0	4.1	4.0	1.0	4.0 ~ 5.0
i_comm3	Everyone voiced their concerns whenever they felt necessary	101	5	0	4.0	4.0	1.1	3.0 ~ 5.0
i_iden1	There were clear expectations of each group member	101	1	0	3.4	3.0	1.0	3.0 ~ 4.0
i_iden2	A reasonable alternative trip existed in case of disagreements	101	1	0	3.8	4.0	1.2	3.0 ~ 5.0
i_iden3	Everyone was happy with the decisions that were made	101	4	0	4.3	4.0	1.0	4.0 ~ 5.0
i_anom1	The group decisions at the decision points were unanimous	100	3	1	4.0	4.0	1.1	4.0 ~ 5.0
i_anom2	Someone tried to impress others.	101	1	0	4.1	4.0	1.0	4.0 ~ 5.0
i_anom3	Love stories were going on in the group	101	6	0	4.1	5.0	1.4	3.0 ~ 5.0
i_anom4	The presence of other groups impacted my group’s decision making	101	2	0	4.1	5.0	1.2	3.0 ~ 5.0
* number of cases minus number of NA
† IDN: Don’t know

Descriptive statistics for without-leader group (long)

					Central tendency		Dispersion tendency
var	Question	n*	n of IDN†	n of NA	Mean	Median	SD	Q1~Q3
i_skill2	There was no large gap in avalanche assessment skills between the group members	114	0	0	3.2	3.0	1.3	2.0 ~ 4.0
i_skill3	There was no important difference in skiing skill level between group members, given the terrain	114	0	0	3.6	4.0	1.3	2.0 ~ 5.0
i_skill4	All group members were equipped with standard avalanche safety equipment (beacon, shovel, probe) and trained in the use of it	114	1	0	4.5	5.0	1.0	4.0 ~ 5.0
i_orga1	The group members knew each other well	113	0	1	4.2	5.0	1.0	4.0 ~ 5.0
i_orga2	The group size was appropriate for the trip (time, difficulty)	113	1	1	4.6	5.0	0.8	4.0 ~ 5.0
i_orga3	The roles of the group members were clearly defined	113	5	1	3.2	3.0	1.4	2.0 ~ 5.0
i_comm1	Decisions concerning avalanche hazard were well discussed in the group	114	0	0	4.0	4.0	1.0	4.0 ~ 5.0
i_comm2	Everyone in the group understood the decisions that were made	114	1	0	4.3	5.0	0.9	4.0 ~ 5.0
i_comm3	Everyone voiced their concerns whenever they felt necessary	114	6	0	4.3	4.0	1.0	4.0 ~ 5.0
i_iden1	There were clear expectations of each group member	114	0	0	3.6	4.0	1.0	3.0 ~ 4.0
i_iden2	A reasonable alternative trip existed in case of disagreements	114	1	0	3.9	4.0	1.1	3.0 ~ 5.0
i_iden3	Everyone was happy with the decisions that were made	114	1	0	4.4	5.0	0.8	4.0 ~ 5.0
i_anom1	The group decisions at the decision points were unanimous	114	7	0	4.2	4.0	1.1	4.0 ~ 5.0
i_anom2	Someone tried to impress others.	114	2	0	4.2	4.0	1.1	4.0 ~ 5.0
i_anom3	Love stories were going on in the group	114	2	0	4.3	5.0	1.2	4.0 ~ 5.0
i_anom4	The presence of other groups impacted my group’s decision making	114	1	0	3.8	4.0	1.4	2.0 ~ 5.0
* number of cases minus number of NA
† IDN: Don’t know

Descriptive statistics for with-leader group (short)

					Central tendency		Dispersion tendency
var	Question	n*	n of IDN†	n of NA	Mean	Median	SD	Q1~Q3
i_skill0	The level of avalanche assessment and rescue skills differed greatly across the group.	101	2	0	2.7	2.0	1.4	2.0 ~ 4.0
i_orga0	The group was well-set up and organized for this trip	101	0	0	3.9	4.0	0.9	3.0 ~ 4.0
i_comm0	The communication in the group was good	101	1	0	4.4	4.0	0.7	4.0 ~ 5.0
i_iden0	The group was cohesive and had a shared vision	100	1	1	4.2	4.0	0.8	4.0 ~ 5.0
i_anom0	Social interactions in the group negatively impacted decision	101	3	0	4.4	5.0	1.0	4.0 ~ 5.0
* number of cases minus number of NA
† IDN: Don’t know

Descriptive statistics for without-leader group (short)

					Central tendency		Dispersion tendency
var	Question	n*	n of IDN†	n of NA	Mean	Median	SD	Q1~Q3
i_orga0	The group was well-set up and organized for this trip	114	0	0	4.1	4.0	0.9	4.0 ~ 5.0
i_comm0	The communication in the group was good	114	0	0	4.3	5.0	1.0	4.0 ~ 5.0
i_iden0	The group was cohesive and had a shared vision	114	0	0	4.2	4.0	0.8	4.0 ~ 5.0
i_anom0	Social interactions in the group negatively impacted decision	113	3	1	4.3	5.0	1.0	4.0 ~ 5.0
* number of cases minus number of NA
† IDN: Don’t know

Adress NA and IDN casewise

The number of NAs and IDNs were few in number comparing with the sample size for each data set. Hence, the NAs and IDNs were checked case-wise, and decisions for each case were made accordingly. Please go to file “NA_and_IDN.md” for full description. A quck summary here: case #82 (in without group) were removed due to high proportion of IDNs, while other cases with NAs/IDNs does not show much logical issue. These NAs/IDNs will be imputed by within-subgroup median.

Sumarize data clensing

The full processes of data cleansing were summarized in the following flowchart.

Flowchart for data cleansing

Visualization

Distribution

Since the data were collected from Likert scale, which usually skewed towards an end, I do not seek normality from these graphs. Instead, I scanned through the distributions to get a sense of the features of each item, such as left skewness (e.g. i_anom3), right skewness (e.g. i_skill4), kurtosis (e.g. i_orga3), polarization (e.g. i_skill3). These also shed light on skiers’ overall performance pattern across sub-groups. To illustrate, it could be interesting to find that the organization of without-leader group wasn’t rated notably lower than that of with-leader group. However, the skills were rated higher in without-leader group. This indicates people who ski without a leader are more confident in his and his teammates skiing/avalanche-forecasting skills. Of course, I hope for a normal distribution from the factor scores obtained by the following factor analysis.

Correlation matrix

Correlation matrix was created for each of the four scales (2 long and 2 short). Pearson correlation coefficients were reported. Any coefficients ≥ 0.3 were highlighted in green circle; any coefficients ≥ 0.3 were highlighted in read circle.

There are several well-recognized criteria for checking factorability, including correlation matrix, KMO test, and Bartlett sphericity test. Here I checked the correlation. Other criteria were checked in the following section. We hope that the majority of the items have a correlation coefficient ≥ 0.3 with at least one other item, which suggest good factorability.

For with-leader group (long), it was observed that 18 of the 20 items correlated at least .3 with at least one other item, suggesting reasonable factorability. See figure 6.

For without-leader group (long), it was observed that 16 of the 17 items correlated at least .3 with at least one other item, suggesting reasonable factorability. See figure 7.

For with-leader group (short), it was observed that 6 of the 6 items correlated at least .3 with at least one other item, suggesting reasonable factorability. See figure 8.

For without-leader group (short), it was observed that 6 of the 6 items correlated at least .3 with at least one other item, suggesting reasonable factorability. See figure 9.

Factor analysis for with-leader group (long)

Check factoribility

KMO i_leader1 0.6334339 i_leader2 0.7072826 i_leader3 0.7506825 i_skill1 0.6608714 i_skill2 0.6974638 i_skill3 0.7299554 i_skill4 0.7616758 i_orga1 0.5801562 i_orga2 0.5211677 i_orga3 0.5329171 i_comm1 0.8067675 i_comm2 0.7224165 i_comm3 0.8089583 i_iden1 0.6324512 i_iden2 0.6075570 i_iden3 0.7061779 i_anom1 0.7318465 i_anom2 0.8095460 i_anom3 0.3640078 i_anom4 0.5455391 Overall 0.6867691

KMO i_leader1 0.6215255 i_leader2 0.7204399 i_leader3 0.7869648 i_skill1 0.6585108 i_skill2 0.7345237 i_skill3 0.7495283 i_skill4 0.7691038 i_orga1 0.6353336 i_orga2 0.5400165 i_orga3 0.5203701 i_comm1 0.8114721 i_comm2 0.7858661 i_comm3 0.8061561 i_iden1 0.6325325 i_iden2 0.6432374 i_iden3 0.7189354 i_anom1 0.7160321 i_anom2 0.8319150 Overall 0.7125075

Results of KMO test of sampling adequacy for with-leader group (long)

	KMO
i_leader1	0.633
i_leader2	0.707
i_leader3	0.751
i_skill1	0.661
i_skill2	0.697
i_skill3	0.730
i_skill4	0.762
i_orga1	0.580
i_orga2	0.521
i_orga3	0.533
i_comm1	0.807
i_comm2	0.722
i_comm3	0.809
i_iden1	0.632
i_iden2	0.608
i_iden3	0.706
i_anom1	0.732
i_anom2	0.810
i_anom3	0.364
i_anom4	0.546
Overall	0.687

Results of KMO test of sampling adequacy for with-leader group (long)

	KMO
i_leader1	0.622
i_leader2	0.720
i_leader3	0.787
i_skill1	0.659
i_skill2	0.735
i_skill3	0.750
i_skill4	0.769
i_orga1	0.635
i_orga2	0.540
i_orga3	0.520
i_comm1	0.811
i_comm2	0.786
i_comm3	0.806
i_iden1	0.633
i_iden2	0.643
i_iden3	0.719
i_anom1	0.716
i_anom2	0.832
Overall	0.713

Results of KMO test of sampling adequacy for with-leader group (long)

	KMO
i_leader1	0.633
i_leader2	0.707
i_leader3	0.751
i_skill1	0.661
i_skill2	0.697
i_skill3	0.730
i_skill4	0.762
i_orga1	0.580
i_orga2	0.521
i_orga3	0.533
i_comm1	0.807
i_comm2	0.722
i_comm3	0.809
i_iden1	0.632
i_iden2	0.608
i_iden3	0.706
i_anom1	0.732
i_anom2	0.810
i_anom3	0.364
i_anom4	0.546
Overall	0.687

Results of KMO test of sampling adequacy for with-leader group (long)

	KMO
i_leader1	0.633
i_leader2	0.707
i_leader3	0.751
i_skill1	0.661
i_skill2	0.697
i_skill3	0.730
i_skill4	0.762
i_orga1	0.580
i_orga2	0.521
i_orga3	0.533
i_comm1	0.807
i_comm2	0.722
i_comm3	0.809
i_iden1	0.632
i_iden2	0.608
i_iden3	0.706
i_anom1	0.732
i_anom2	0.810
i_anom3	0.364
i_anom4	0.546
Overall	0.687

Results of bartlett test for with-leader group (long)

Chi-square	p-value	DF
518.942	<0.001	190

Explore number of factors

## Parallel analysis suggests that the number of factors =  3  and the number of components =  NA

## 
## Number of factors
## Call: vss(x = x, n = n, rotate = rotate, diagonal = diagonal, fm = fm, 
##     n.obs = n.obs, plot = FALSE, title = title, use = use, cor = cor)
## VSS complexity 1 achieves a maximimum of 0.49  with  1  factors
## VSS complexity 2 achieves a maximimum of 0.63  with  3  factors
## The Velicer MAP achieves a minimum of 0.02  with  2  factors 
## Empirical BIC achieves a minimum of  -449.58  with  2  factors
## Sample Size adjusted BIC achieves a minimum of  -38.79  with  5  factors
## 
## Statistics by number of factors 
##   vss1 vss2   map dof chisq    prob sqresid  fit RMSEA  BIC SABIC complex
## 1 0.49 0.00 0.022 170   302 1.8e-09    18.5 0.49 0.088 -481    56     1.0
## 2 0.43 0.61 0.020 151   200 4.9e-03    14.1 0.61 0.056 -496   -19     1.4
## 3 0.41 0.63 0.022 133   159 6.0e-02    11.7 0.68 0.043 -453   -33     1.7
## 4 0.39 0.59 0.026 116   136 1.0e-01    10.6 0.71 0.040 -398   -32     2.0
## 5 0.38 0.58 0.030 100   106 3.2e-01     9.4 0.74 0.022 -355   -39     2.1
##   eChisq  SRMR eCRMS eBIC
## 1    464 0.111 0.117 -319
## 2    246 0.080 0.090 -450
## 3    164 0.066 0.078 -449
## 4    137 0.060 0.077 -397
## 5    106 0.053 0.073 -355

Explore factor solutions

Explore 5-factor solution

Factor loadings of the 5-factor solution for with-leader group (long)

Item	ML2	ML4	ML3	ML5	ML1
i_leader1	-0.448		0.407
i_leader2			0.747
i_leader3		0.556
i_skill1	0.88
i_skill2	0.665
i_skill3	0.327	0.321
i_skill4	0.333
i_orga1		0.527
i_orga2
i_orga3		0.368
i_comm1			0.511
i_comm2	0.385	0.303			0.833
i_comm3		0.649
i_iden1
i_iden2
i_iden3				0.549
i_anom1				0.704
i_anom2		0.413	0.323
i_anom3				0.345
i_anom4

Explore 4-factor solution

Factor loadings of the 4-factor solution for with-leader group (long)

Item	ML1	ML3	ML2	ML4
i_leader1	-0.4		0.42	0.334
i_leader2			0.768
i_leader3		0.598
i_skill1	0.93
i_skill2	0.653
i_skill3	0.348
i_skill4	0.338
i_orga1		0.542
i_orga2
i_orga3		0.389
i_comm1			0.5
i_comm2	0.363	0.382		0.374
i_comm3		0.616
i_iden1
i_iden2
i_iden3		0.342		0.656
i_anom1				0.627
i_anom2		0.41	0.303
i_anom3
i_anom4

Explore 3-factor solution

Factor loadings of the 3-factor solution for with-leader group (long)

Item	ML1	ML3	ML2
i_leader1			0.615
i_leader2			0.689
i_leader3		0.556	0.322
i_skill1	0.929
i_skill2	0.638
i_skill3	0.369
i_skill4	0.392
i_orga1		0.518
i_orga2		0.301
i_orga3		0.445
i_comm1	0.358		0.384
i_comm2	0.403	0.471	0.31
i_comm3		0.494
i_iden1		0.378
i_iden2
i_iden3		0.484	0.37
i_anom1			0.435
i_anom2		0.398	0.387
i_anom3
i_anom4

Finetune 3-factor solution

Factor loadings of the 3-factor solution for with-leader group (long)

Item	ML2	ML1	ML3
i_leader1	0.614	-0.356
i_leader2	0.613
i_leader3	0.344		0.589
i_skill1		0.925
i_skill2		0.651
i_skill4		0.355
i_orga1			0.598
i_comm3			0.596
i_iden2	0.332
i_iden3	0.46		0.388
i_anom1	0.515
i_anom2	0.414		0.402

Explore 2-factor solution

Factor loadings of the 2-factor solution for with-leader group (long)

Item	ML2	ML1
i_leader1	0.528
i_leader2	0.385
i_leader3	0.581
i_skill1		0.957
i_skill2		0.635
i_skill3		0.416
i_skill4		0.374
i_orga1
i_orga2		0.322
i_orga3	0.397
i_comm1		0.348
i_comm2	0.467	0.509
i_comm3	0.47
i_iden1	0.324
i_iden2	0.313
i_iden3	0.591
i_anom1	0.477	0.318
i_anom2	0.537
i_anom3
i_anom4

Finetune 2-factor solution

Factor loadings of the 3-factor solution for with-leader group (long)

Item	ML2	ML1
i_leader2	0.361
i_leader3	0.755
i_skill1		0.898
i_skill2		0.671
i_skill3		0.37
i_orga1	0.312
i_comm1	0.332
i_comm2	0.559	0.382
i_comm3	0.593
i_iden2
i_anom1	0.386

Comparison between factor solutions, with-leader (long)

Comparison between factor solutions, with-leader (long)

	CumulativeVariance
2-factor(tuned)	0.329
2-factor	0.265
3-factor(tuned)	0.403
3-factor	0.317
4-factor	0.352
5-factor	0.396

Check the factor connotation for 3-factor solution (fine-tuned)

Final items for 3 factor solution, with-leader group (long)

	Item
ML2: Leadership Quality
i_iden2	A reasonable alternative trip existed in case of disagreements
i_leader3	Everyone could voice their concerns to the leader (formal or informal)
i_anom1	The group decisions at the decision points were unanimous
i_leader1	The leader (formal or informal) was the best suited person in the group to make the decisions.
i_leader2	The leader (formal or informal) communicated openly and clearly
i_comm3	Everyone voiced their concerns whenever they felt necessary
i_comm2	Everyone in the group understood the decisions that were made
ML3: Planning
i_orga1	The group members knew each other well
i_skill1	The least knowledgeable group member could conduct satisfactory avalanche assessments for this trip
ML1: Skill
i_skill2	There was no large gap in avalanche assessment skills between the group members
i_skill4	All group members were equipped with standard avalanche safety equipment (beacon, shovel, probe) and trained in the use of it

Factor analysis for with-leader group (short)

Check factoribility

Results of KMO test of sampling adequacy for with-leader group (short)

	KMO
i_leader0	0.808
i_skill0	0.639
i_orga0	0.727
i_comm0	0.755
i_iden0	0.700
i_anom0	0.783
Overall	0.735

Results of bartlett test for with-leader group (short)

Chi-square	p-value	DF
94.2	<0.001	15

Explore number of factors

## Parallel analysis suggests that the number of factors =  1  and the number of components =  NA

## 
## Number of factors
## Call: vss(x = x, n = n, rotate = rotate, diagonal = diagonal, fm = fm, 
##     n.obs = n.obs, plot = FALSE, title = title, use = use, cor = cor)
## VSS complexity 1 achieves a maximimum of 0.69  with  2  factors
## VSS complexity 2 achieves a maximimum of 0.73  with  2  factors
## The Velicer MAP achieves a minimum of 0.05  with  1  factors 
## Empirical BIC achieves a minimum of  -32.85  with  1  factors
## Sample Size adjusted BIC achieves a minimum of  -5.89  with  1  factors
## 
## Statistics by number of factors 
##   vss1 vss2   map dof   chisq prob sqresid  fit RMSEA BIC SABIC complex  eChisq
## 1 0.61 0.00 0.047   9 7.1e+00 0.62     3.3 0.61     0 -34  -5.9     1.0 8.6e+00
## 2 0.69 0.73 0.119   4 1.6e+00 0.81     2.3 0.73     0 -17  -4.2     1.1 1.8e+00
## 3 0.53 0.70 0.233   0 9.6e-02   NA     2.1 0.76    NA  NA    NA     1.4 1.2e-01
## 4 0.48 0.68 0.431  -3 5.0e-11   NA     1.8 0.79    NA  NA    NA     1.6 6.8e-11
## 5 0.45 0.61 1.000  -5 0.0e+00   NA     1.6 0.81    NA  NA    NA     1.8 5.3e-16
## 6 0.44 0.60    NA  -6 4.8e+00   NA     2.9 0.65    NA  NA    NA     1.8 5.2e+00
##      SRMR eCRMS eBIC
## 1 5.4e-02 0.069  -33
## 2 2.5e-02 0.048  -17
## 3 6.3e-03    NA   NA
## 4 1.5e-07    NA   NA
## 5 4.2e-10    NA   NA
## 6 4.1e-02    NA   NA

Explore 2-factor solution

Figure 16. Factor loadings of the 5-factor solution for with-leader group (short)

Item	ML2	ML1
i_leader0	0.485
i_skill0		0.993
i_orga0	0.566
i_comm0	0.504
i_iden0	0.855
i_anom0	0.421

fine-tune 2-factor solution

Factor loadings of the 3-factor solution for with-leader group (long)

Item	ML2	ML1
i_iden0	0.838
i_comm0	0.522
i_leader0	0.483
i_orga0	0.574
i_skill0		0.993

Explore 3-factor solution

Factor loadings of the 5-factor solution for with-leader group (long)

Item	ML1	ML3	ML2
i_leader0		0.487
i_skill0
i_orga0	0.947
i_comm0			0.869
i_iden0	0.311	0.664
i_anom0		0.478

Factor analysis for without-leader group (short)

Check factoribility

Results of KMO test of sampling adequacy for without-leader group (short)

	KMO
i_skill0	0.805
i_orga0	0.808
i_comm0	0.799
i_iden0	0.820
i_anom0	0.793
Overall	0.805

Results of bartlett test for with-leader group (short)

Chi-square	p-value	DF
172.282	<0.001	10

Explore number of factors

## Parallel analysis suggests that the number of factors =  1  and the number of components =  NA

## 
## Number of factors
## Call: vss(x = x, n = n, rotate = rotate, diagonal = diagonal, fm = fm, 
##     n.obs = n.obs, plot = FALSE, title = title, use = use, cor = cor)
## VSS complexity 1 achieves a maximimum of 0.83  with  1  factors
## VSS complexity 2 achieves a maximimum of 0.89  with  2  factors
## The Velicer MAP achieves a minimum of 0.08  with  1  factors 
## Empirical BIC achieves a minimum of  -16.67  with  1  factors
## Sample Size adjusted BIC achieves a minimum of  0.44  with  2  factors
## 
## Statistics by number of factors 
##   vss1 vss2   map dof   chisq  prob sqresid  fit RMSEA   BIC SABIC complex
## 1 0.83 0.00 0.076   5 1.0e+01 0.067    1.55 0.83 0.096 -13.4  2.42     1.0
## 2 0.66 0.89 0.188   1 2.0e+00 0.156    1.04 0.89 0.094  -2.7  0.44     1.5
## 3 0.46 0.79 0.389  -2 3.1e-12    NA    0.92 0.90    NA    NA    NA     1.9
##    eChisq    SRMR eCRMS  eBIC
## 1 7.0e+00 5.5e-02 0.078 -16.7
## 2 8.7e-01 2.0e-02 0.062  -3.9
## 3 1.2e-12 2.3e-08    NA    NA

Explore 2-factor solution

Figure Factor loadings of the 5-factor solution for without-leader group (short)

Item	ML1	ML2
i_skill0		0.72
i_orga0	0.546	0.513
i_comm0	0.691
i_iden0	0.53	0.48
i_anom0	0.721

s ### Explore 3-factor solution

Factor loadings of the 5-factor solution for with-leader group (long)

Item	ML2	ML3	ML1
i_skill0	0.637
i_orga0	0.551	0.301	0.448
i_comm0		0.444	0.594
i_iden0	0.574	0.479
i_anom0		0.702	0.307